Matrix realignment and partial transpose approach to entangling power of quantum evolutions

Unifying several separability conditions using the covariance matrix criterion

We present a framework for deciding whether a quantum state is separable or entangled using covariance matrices of locally measurable observables. This leads to the covariance matrix criterion as a general separability criterion. We demonstrate that this criterion allows to detect many states where the familiar criterion of the positivity of the partial transpose fails. It turns out that a large number of criteria which have been proposed to complement the positive partial transpose criterion - the computable cross norm or realignment criterion, the criterion based on local uncertainty relatio…

通过部分转置和重排矩量化混合态纠缠

Quantifying mixed-state entanglement via partial transpose and realignment moments

本文提出基于部分转置和重排矩的纠缠见证子，可高效测量并用于测试混合态施密特秩、认证量子电路深度等，为大型带噪声量子系统的纠缠量化提供新方法。

PPT和CCNR准则的量子电路实现

Quantum Circuit Realization of the PPT and CCNR Criteria

提出基于PPT和CCNR准则的量子电路实现方案，通过SWAP操作和变分量子奇异值分解子程序高效检测纠缠。

Is absolute separability determined by the partial transpose?

The absolute separability problem asks for a characterization of the quantum states $ρ\in M_m\otimes M_n$ with the property that $UρU^\dagger$ is separable for all unitary matrices $U$. We investigate whether or not it is the case that $ρ$ is absolutely separable if and only if $UρU^\dagger$ has positive partial transpose for all unitary matrices $U$. In particular, we develop an easy-to-use method for showing that an entanglement witness or positive map is unable to detect entanglement in any such state, and we apply our method to many well-known separability criteria, including the range cri…

Quantum Dynamics of Bound Entangled States

By using the partial transpose and realignment method,we study the time evolution of the bound entanglement under the bilinear-biquadratic Hamiltonian. For the initial Horodecki's bound entangled state, it keeps bound entangled for some time, while for the initial bound entangled states constructed from the unextendable product basis, they become free once the time evolution begins. The time evolution provides a new way to construct bound entangled states, and also gives a method to free bound entanglement.

基于矩的纠缠判据与度量

Moments based entanglement criteria and measures

本文提出两种基于矩阵矩的易用纠缠判据，给出可实验测量的 concurrence 下界，并构建两体及真正三体纠缠度量，能更细致地刻画纠缠。

Entanglement measures of bipartite quantum gates and their thermalization under arbitrary interaction strength

Entanglement properties of bipartite unitary operators are studied via their local invariants, namely the entangling power $e_p$ and a complementary quantity, the gate typicality $g_t$. We characterize the boundaries of the set $K_2$ representing all two-qubit gates projected onto the plane $(e_p, g_t)$ showing that the fractional powers of the \textsc{swap} operator form a parabolic boundary of $K_2$, while the other bounds are formed by two straight lines. In this way a family of gates with extreme properties is identified and analyzed. We also show that the parabolic curve representing powe…

Multipartitioning topological phases by vertex states and quantum entanglement

We discuss multipartitions of the gapped ground states of (2+1)-dimensional topological liquids into three (or more) spatial regions that are adjacent to each other and meet at points. By considering the reduced density matrix obtained by tracing over a subset of the regions, we compute various correlation measures, such as entanglement negativity, reflected entropy, and associated spectra. We utilize the bulk-boundary correspondence to show that such multipartitions can be achieved by using what we call vertex states in (1+1)-dimensional conformal field theory -- these are a type of state use…